[Risolto] Limite di successione

* lim_(n → ∞) (sin(5/n) + 1/e^n)/(tan(3/n) - 4/n^2) =
= lim_(n → ∞) sin(5/n)/(tan(3/n) - 4/n^2) + lim_(n → ∞) (1/e^n)/(tan(3/n) - 4/n^2) =
= lim_(n → ∞) sin(5/n)*cos(3/n)/(sin(3/n) - 4*cos(3/n)/n^2) + 0 =
= (lim_(n → ∞) cos(3/n)) * lim_(n → ∞) sin(5/n)/(sin(3/n) - 4*cos(3/n)/n^2) =
= (1) * lim_(n → ∞) sin(5/n)/(sin(3/n) - 0) =
= lim_(n → ∞) sin(5/n)/sin(3/n) =
= 5/3
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DETTAGLI
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* lim_(n → ∞) sin(5/n)/sin(3/n) =
= lim_(n → ∞) (d/dn sin(5/n))/(d/dn sin(3/n)) =
= lim_(n → ∞) (- 5*cos(5/n)/n^2)/(- 3*cos(3/n)/n^2) =
= lim_(n → ∞) 5*cos(5/n)/(3*cos(3/n)) =
= 5/3
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* lim_(n → ∞) (1/e^n)/(tan(3/n) - 4/n^2) =
= lim_(n → ∞) 1/(((e^n)*tan(3/n))*(1 - 4*tan(3/n)/n^2)) =
= lim_(n → ∞) 1/(((e^n)*tan(3/n))*(1 - 4*tan(3/n)/n^2)) =
= lim_(n → ∞) 1/((e^n)*tan(3/n)) =
= lim_(n → ∞) cos(3/n)/((e^n)*sin(3/n)) =
= lim_(n → ∞) e^(- n)/sin(3/n) =
= ... =
= 0